Penalized empirical likelihood for partially linear errors-in-variables panel data models with fixed effects

For the partially linear errors-in-variables panel data models with fixed effects, we, in this paper, study asymptotic distributions of a corrected empirical log-likelihood ratio and maximum empirical likelihood estimator of the regression parameter. In addition, we propose penalized empirical likelihood (PEL) and variable selection procedure for the parameter with diverging numbers of parameters. By using an appropriate penalty function, we show that PEL estimators have the oracle property. Also, the PEL ratio for the vector of regression coefficients is defined and its limiting distribution is asymptotically chi-square under the null hypothesis. Moreover, empirical log-likelihood ratio for the nonparametric part is also investigated. Monte Carlo simulations are conducted to illustrate the finite sample performance of the proposed estimators.